CHICAGO – Officially, open season for finding a new Timberwolves coach began nearly a month ago, when the team announced Rick Adelman’s retirement.

In reality, it won’t truly start until Tuesday night.

That’s when the NBA holds its annual draft lottery, its annual game of luck in which the Wolves have less than a 1 percent chance to leap from their 13th overall draft position into the top three or lose their pick altogether to Phoenix because of a prior trade arrangement.

By then, Wolves president of basketball operations Flip Saunders will know if his team finally has beaten the lotto odds — and very long ones at that — for the first time in the franchise’s 26-year history.

By then, he also will know much better just what kind of roster he will have to offer a prospective coach … or himself.

So far, Saunders has conducted his search under a cloak of secrecy because he says that’s the way he wanted it done every time he was hired as a head coach.

Gleaned from conversations with league executives and agents at last week’s NBA draft combine in Chicago, this much is known so far about Saunders’ shadowy maneuverings:

• He interviewed former Memphis coach Lionel Hollins for the job approaching three weeks ago now but has proceeded no further with a candidate now in the running for the Cleveland opening.

• He kicked the tires — inquiring about their interest through conversations without formal interviews — on college coaches Tom Izzo and Fred Hoiberg as well as veteran NBA coach Stan Van Gundy, but discussions didn’t go beyond that.

• At this point, Saunders doesn’t appear interested in 1,000-game winner George Karl, who very much wants to coach again but would prefer jobs in Cleveland and Washington (should the Wizards job open). But Saunders very well could opt for a NBA career coach — such as a P.J. Carlesimo or Scott Skiles — who fits his criteria for head-coaching experience as well as an ability to develop Ricky Rubio and answer questions every day next season about Kevin Love’s future.

Nearly a month after Adelman retired, there’s also the possibility that after doing all his homework, Saunders will decide he’s the best man for the job.

That only will happen, though, if he convinces owner Glen Taylor than he can — and should — do both jobs.

Saunders just might do so if he also convinces Taylor he’s the best chance to keep Love in Minnesota after he becomes an unrestricted free agent in July 2015.

Some unexpected lottery luck Tuesday conceivably could convince Love to stay and Saunders to insist on the coaching job as well. Lacking that, the way the lottery balls fall — and how teams such as the Lakers and Celtics fare — could instead soften Saunders’ resolve and get him to consider trading Love by draft night if the Lakers or Celtics have a very high pick to dangle.

“Like that squirt-it drink,” an NBA coaching source said, certain that Saunders won’t get serious about his coaching search until he knows if the Wolves get lucky Tuesday or not. “It changes everything.”

To interject a note of reality here: The Wolves have little more than a 2 percent chance of moving from the 13th pick into the draft’s top three.

They have a half-percent chance of losing their pick this year: If Phoenix beats the odds and moves from No. 14 into the top three, the Wolves will drop from 13 to 14 and thus lose a top-13 protected pick they owe the Suns for a 2012 trade.

They agreed to give Phoenix a future first-round pick if the Suns took on former lottery pick Wes Johnson’s contract so the Wolves could clear enough salary-cap room to sign free-agent Andrei Kirilenko, who stayed just one season in Minnesota.

Saunders and his scouting staff attended last week’s NBA draft combine in Chicago, where most of the top prospects were measured, tested and interviewed by individual teams.

Those top prospects also had the chance to interview team personnel right back, and Creighton forward Doug McDermott — a possible choice at No. 13 — said he spoke with the Wolves about their search for a new coach.

“I want to be real comfortable with the coach,” McDermott said. “A general manager can be comfortable with you, but at the end of the day, the coach is the guy who puts you on the floor.

“So before I get to any team, I want to know that the coach is as big a fan as the GM.”

Saunders has said he has no timetable to hire a coach — who will be selected partly for his ability to nurture Rubio — and says it doesn’t necessarily need to happen before the draft.

“It matters maybe a little bit,” said Michigan guard Nik Stauskas, another potential pick at No. 13, “because you don’t know the direction they’re headed and the style of play that they’re really going to get after it with.’’

The Wolves interviewed a smattering of players they could take with the 13th pick, and some that have no chance of falling that far.

Kentucky forward Julius Randle is one of those players who won’t make it out of the draft’s top 10. He interviewed with the Wolves and said their lack of a coach wouldn’t be a concern.

“Everything about success depends on an organization and the personnel they have there with their GM, their owner,” Randle said. “If they have a winning attitude, I feel like they always will pick the right person.”

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